5

Point) Indicate whether the following statement is true or false.1. If the set of vectors U spans a subspace S, then vectors can be added to U to create a basis for...

Question

Point) Indicate whether the following statement is true or false.1. If the set of vectors U spans a subspace S, then vectors can be added to U to create a basis for $

point) Indicate whether the following statement is true or false. 1. If the set of vectors U spans a subspace S, then vectors can be added to U to create a basis for $



Answers

Determine whether each statement is true or false. If the dot product of two nonzero vectors is equal to zero, then the vectors must be perpendicular.

In this video, we're gonna be selling problem number 24 of section four point would. And, um, this is basically a five part question where were in each part of us? US. Approved, whether given same is true or false. So, um, the first statement says that it for a it's 24 aces, that a vector is any element of the vector space. And this is true because it is the definition of a vector. And, um, it is listed under the definition of the vector space in the book. So we know that a vector is any element of electric space. Um, which basically just means that, um, which basically just means that if a vector contains, like, let's, say, three countries, any vector in, um the vector space that is three dimensional because of three column entries would would also be a vector. So this thing that is true B says that if you if you is a vector in a vector space V than negative one, you is the same as negative you. So it's basically just saying that negative u equals negative one times you. If you look at Axiom number 10 on the first page of the chapter, Section 4.1. It says that one U equals you. So if you multiply this by a negative one, we got negative one U equals negative. You. So this is true. Um, see, Asa's states that a vector space is also a subspace. And this is true because we know that we know that, um, every set is a subset of itself. So seeing the definition of a vector space, you know that every vector spaces subspace of itself, and it is listed in the second paragraph. Um, after the definition of a vector space in this section. Okay, Um, uh, d states that are two of the subspace of our three. And this is false, because if you look at example eight. Um, we know that our two is not not even a subset of our three because there were talking about two different dimensions. Um, and because elements of our two have two entries in them, 12 and elements of our three have three column entries. We know that this demon is false, and the last one states that, um e a subset age of vector space via subspace of we um, if the following conditions are satisfied, the zero backer of E is an h u v e com movie, and you plus a v e r N h um, See is a scaler and see you as an H. So this is tricky as this is Basie how we test if something is a subspace of another vector space. So I stayed in the conditions two and three. Um, the conditions don't make sense because it doesn't say that the vectors u n Veer actually, um, conditions for this statement to be true. So to be correct, you have toe you have toe say that for every U. N V in H in a couple of places. So this definition is incomplete. It's missing some words. Um, so it is not so here. Um, the definition of two which says you come Avi and duplicity yarn h and sees a scaler and see you as an h, um are false because, um, because these vectors also have to be an age when there's killed by any value are added thio Any other vector? Um, that that is from the subspace of age that exists in the vector space of age. So this is also false

Okay. This question asks us if the dot product returns a scaler. So the dot product is usually defined as just multiplying like components and then adding them together. And we see that this is a number so not a factor. And that means that this is a scaler quantity. So the claim is true.

So in again. Question. If we and be a non Jew directors, then the orthogonal production off Viane be its director. That is peddled. Toby reacted with this. A statement we have toe are we have to find the disconnect or not. So let's let's assume there is a vector the vector. And there is a rector be vector light. So if we find the production off director on be vector, then the production will be like this. Like, this is the vector, and this is be vectors off the production off we worked on. We will be, uh, in this direction, which is parallel to the direction off the reactor. Right. So the given courage statement ISC, uh, toe

The questions is the two vectors U equals zero common zero on V equals minus 12. Former six when U and V are part the land. Now this statement is true because the victor zero is 4 to 1. Every other victor does. This statement is true.


Similar Solved Questions

5 answers
Electo: wos b3undi 6p pon 64 Me Projltoho 0 Aorce roekQ Lho^ 4ke elect^C bice 61 delemre {Ve no4:J> o4 exerd 04 tle 6s 36i1 _
electo: wos b3undi 6p pon 64 Me Projltoho 0 Aorce roekQ Lho^ 4ke elect^C bice 61 delemre {Ve no4:J> o4 exerd 04 tle 6s 36i1 _...
5 answers
1 5Help?ol the1 2 1
1 5 Help? ol the 1 2 1...
5 answers
(24 points) When certain defective die is tossed; the numbers from 1-6 will be On the top face With the following probabilities: P4Find the probability that (6 pts) An even number is on top(6 pts) Anon-prime number is on top(6 pts) A number less than is on top(6 pts) A number greater than 2 is on top
(24 points) When certain defective die is tossed; the numbers from 1-6 will be On the top face With the following probabilities: P4 Find the probability that (6 pts) An even number is on top (6 pts) Anon-prime number is on top (6 pts) A number less than is on top (6 pts) A number greater than 2 is o...
1 answers
GahorAIAE?nadcna Irvey heaop oliatdd Ano eoean ccCILAgE rcAE Lnd GaKEoetor Taib and Lhe Dercenteol Kno got ont According Ine !Uryey aal Tamcneryie Ed Ooeeenad eaeeomor tne men who had asked for raice reclivld the raise slecued random (rom Wnl Suryly copulalion Men,Ond tnc {cllowino probepilities (Enter Yovr answens three cecima places TaDandPiman Oskcd forToisc)Arnan reccivcdOwvenasked(c) A{man as*cdraise Jnd reccived risc)
Gahor AIAE? nadcna Irvey heaop oliatdd Ano eoean ccCILAgE rcAE Lnd GaKEoetor Taib and Lhe Dercenteol Kno got ont According Ine !Uryey aal Tamcneryie Ed Ooeeenad eaeeomor tne men who had asked for raice reclivld the raise slecued random (rom Wnl Suryly copulalion Men,Ond tnc {cllowino probepilities (...
5 answers
Point) Find the sum of the following series. If it is divergent; type "Diverges" or D". 1 1 1 (3)" = 1 + + n 32 192 1024 n=1 Answer:Note: You cannot write a decimal number for the answer:Hint: What power series is equal to this sum?
point) Find the sum of the following series. If it is divergent; type "Diverges" or D". 1 1 1 (3)" = 1 + + n 32 192 1024 n=1 Answer: Note: You cannot write a decimal number for the answer: Hint: What power series is equal to this sum?...
5 answers
5) Design a synthesis # synthesis of ethoxy [email protected] ethane: You can use any other rengents You want points)
5) Design a synthesis # synthesis of ethoxy [email protected] ethane: You can use any other rengents You want points)...
5 answers
Which of the following organisms is responsible for Chagas- disease?Giardia sp_Saccharomyces cereviase,Trypanosoma cruziiPlasmodium falciparum
Which of the following organisms is responsible for Chagas- disease? Giardia sp_ Saccharomyces cereviase, Trypanosoma cruzii Plasmodium falciparum...
5 answers
Use Ihe prph polnrtnriu Anlarcont_ Iny mnlTna CamainUlo inlanallnotatot
Use Ihe prph polnrtnriu Anlarcont_ Iny mnl Tna Camain Ulo inlanallnotatot...
5 answers
Pancreas secretes(a) Insulin(b) Glucagon(c) Enzymes(d) All of these
Pancreas secretes (a) Insulin (b) Glucagon (c) Enzymes (d) All of these...
5 answers
Sketch the graph of the function by making a table of values. Use a calculator if necessary.$$f(x)=2^{x}$$
Sketch the graph of the function by making a table of values. Use a calculator if necessary. $$f(x)=2^{x}$$...
5 answers
Find f "(a).Kt) = 2+49 t + 8Part 0f 3To find f"(a), we will use the formula 6 "(a) Ilm IO) fe)Since (t) = 3tk49 we have (+ 8F(a) IlmPutting " the (ractions In the numerator over common denominator and simplifylng, we have 344 J12 (3t 19)( [+ 8 (3a 19)(t + 8) (t + 8)(a Jta + 19a + 24t + 152 _ Bat _ 49 _ 2ta 452 8)(a + 8)8)(a + 8)
Find f "(a). Kt) = 2+49 t + 8 Part 0f 3 To find f"(a), we will use the formula 6 "(a) Ilm IO) fe) Since (t) = 3tk49 we have (+ 8 F(a) Ilm Putting " the (ractions In the numerator over common denominator and simplifylng, we have 344 J12 (3t 19)( [+ 8 (3a 19)(t + 8) (t + 8)(a Jta +...
3 answers
(12 points) Let A be countable subset of R Show that there is aeR such that (a+A)oA= $, where R is the set of all real numbers.
(12 points) Let A be countable subset of R Show that there is aeR such that (a+A)oA= $, where R is the set of all real numbers....
5 answers
Gunbunetni upccieru oatitytcnnemonchTebil Ecmeaclcdutcn
Gunbunetni upccieru oatity tcnne monchTebil Ecmeaclc dutcn...
5 answers
If the bond energy for the C?H bond is 413 kJ/mol, how much energy is needed to break all the bonds in 1.0 mol of methane molecules?
If the bond energy for the C?H bond is 413 kJ/mol, how much energy is needed to break all the bonds in 1.0 mol of methane molecules?...
5 answers
2) Find the volume created by stacking isosceles right triangles along the x-axis from x 0 to x TT so that the height of the triangle at the point x is sin(x).
2) Find the volume created by stacking isosceles right triangles along the x-axis from x 0 to x TT so that the height of the triangle at the point x is sin(x)....

-- 0.021602--